Advanced communications applications that are now a routine part of everyday life, such as cellular telephones, wireless networks, satellite broadcasting and fiber-optic communication, rely on continuing advances in the electronic and related arts in connection with increased speed and reduced size; namely, increasing the speed of information transmission and miniaturizing the integrated circuits that perform various communication-related functions. However, as system designers look forward to using higher frequencies in the range of tens of gigahertz (GHz), as well as the miniaturization of integrated circuits toward an atomic scale, a number of aspects of conventional integrated circuit technology continue to become inapplicable and obsolete. Thus, a common design challenge involves finding new ways to implement well-known circuit building blocks for faster operation, and often in a smaller space. In some instances, such implementations may exploit electromagnetic wave-base concept, and involve a transmission line or waveguide configuration fabricated on a semiconductor substrate.
Transmission line theory is well-established in the art. Generally speaking, a transmission line provides a means by which power or information may be transmitted in a guided manner, for example, to connect a signal source to a load. A transmission line typically includes two parallel conductors separated by a dielectric material. Signals propagate along a given transmission line as electromagnetic waves, and various physical parameters relating to the transmission line, as well as parameters relating to the source of the signal on the line and any loads on the line, affect wave propagation.
FIGS. 1a–1e illustrate typical examples of transmission lines, including a coaxial cable (FIG. 1a), a two-wire line (FIG. 1b), a parallel-plate or planar line (FIG. 1c), a wire above a conducting plane (FIG. 1d), and a microstrip line (FIG. 1e). Again, it is noteworthy that each of these examples consists of two conductors in parallel. Coaxial cables routinely are used in electrical laboratories and in several common consumer applications to interconnect various electrical apparatus (e.g., connecting TV sets to TV antennas or cable feeds). Microstrip lines are particularly important in integrated circuits based on various semiconductor fabrication techniques, where parallel metallic strips fabricated on a dielectric substrate (i.e., separated by a dielectric) connect electronic elements.
Transmission lines often are regarded as special cases of a wider category of “waveguides.” A waveguide refers generally to a system that is configured to guide electromagnetic radiation from one point to another. In several common applications, however, a waveguide is more specifically regarded essentially as a bounded conduit through which electromagnetic radiation propagates in a somewhat more confined manner than that generally considered in connection with transmission lines. For example, in the microwave regime, unlike a two-conductor transmission line, a waveguide may be formed as a hollow metallic pipe or tube that may be rectangular, elliptical, or circular in cross-section. In the optical regime, which is not supported at all by transmission lines, waveguides often are formed as a solid dielectric filament (e.g., an optical fiber) or a thin dielectric film bounded by a lower refractive index environment.
As conventionally treated in many applications, transmission lines often may be characterized somewhat differently from a wider category of waveguides in some significant respects. For example, first, a transmission line generally may be configured to operate from DC (frequency f=0) to very high frequencies (e.g., in the millimeter and microwave range, from about 1 GHz to 100 GHz); however, a waveguide can only operate above a certain frequency (a “cutoff frequency”) determined by its particular construction and dimensions, and therefore acts generally as a high-pass filter. On the other hand, at significantly high frequencies on the order of approximately 50 GHz to 300 GHz, transmission lines conventionally are regarded as becoming generally inefficient due to the well-known skin effect in the transmission line conductors, as well as dielectric losses involving the material separating the conductors; in contrast, waveguides conventionally are considered in this range of frequencies to obtain larger bandwidth and lower signal attenuation (i.e., a wider range of frequency response with lower signal power loss). However, at the lower end of this frequency range and below, waveguides conventionally are considered to become excessively large in size for some applications, especially integrated circuit applications in which increased miniaturization typically is a goal. Yet another difference between transmission lines and waveguides is that a transmission line can only support a transverse electromagnetic (TEM) wave (i.e., a wave in which both the electric and magnetic field are oriented transversely to the direction of wave propagation), whereas a waveguide generally can support many possible field configurations (i.e. modes).
In semiconductor fabrication of microelectronic circuits, waveguides and transmission lines for carrying high frequency electronic signals conventionally have been implemented in a variety of ways. Two such implementations are referred to respectively as a coplanar waveguide (CPW) and a coplanar stripline (CPS). FIGS. 2A and 2B show different views of a coplanar waveguide, while FIGS. 3A and 3B show different views of a coplanar stripline.
In particular, FIG. 2A illustrates a cross-sectional view of a coplanar waveguide 50 formed by three parallel conductors 20A, 40, and 20B disposed on a dielectric layer 101 on a semiconductor substrate 103. FIG. 2B shows a top view looking down onto an exemplary coplanar waveguide device, in which the center conductor 40 is terminated on each end with pads 42A and 42B, and the conductors 20A and 20B are shown to be electrically connected so as to completely surround the conductor 40 in the plane (the cross-sectional view of FIG. 2A is taken along the dashed lines 2A—2A in FIG. 2B). As illustrated in both FIGS. 2A and 2B, a width W1 of the conductors 20A and 20B may be significantly greater than a width W2 of the center conductor 40.
During normal operation, the conductors 20A and 20B of the coplanar waveguide 50 are electrically connected together to a ground or reference potential, and the signal to be transmitted is applied to the center conductor 40. In this respect, it is particularly noteworthy that the respective ground and signal conductors in a coplanar waveguide are not symmetric, as the combined ground conductors 20A and 20B cover a significantly larger area than the center signal conductor 40. This configuration commonly is referred to as an “unbalanced” configuration. The arrangement of a large ground or reference potential surrounding the center signal conductor 40 serves to confine the electric field in the regions between the center conductor and the ground or reference conductors, thereby creating the “conduit” through which the wave may propagate.
In contrast to a coplanar waveguide, a coplanar stripline is a symmetric or balanced two-conductor device. FIGS. 3A and 3B show different perspectives of one example of an idealized infinite coplanar stripline 100 made up of two substantially identical parallel conductors 100A and 100B separated by a distance S. In particular, FIG. 3A shows a cross-section of the conductors 100A and 100B which, for example, may be metal lines disposed above the dielectric layer 101 on the substrate 103. FIG. 3B shows a top view looking down onto the conductors disposed on the substrate (the cross-sectional view of FIG. 3A is taken along the dashed lines 3A—3A in FIG. 3B).
As can be readily observed in FIGS. 3A and 3B, the geometry of the coplanar stripline 100 is significantly different from that of the coplanar waveguide 50 shown in FIGS. 2A and 2B. In particular, the coplanar waveguide 50 includes three conductors in cross-section, whereas the coplanar stripline 100 includes only two conductors. Moreover, unlike the ground conductors 20A and 20B and the center signal conductor 40 of the coplanar waveguide, which may have respectively different widths, the conductors 100A and 100B of the coplanar stripline have substantially identical widths W3, as indicated in FIGS. 3A and 3B. Again, this arrangement of substantially identical parallel conductors in the coplanar stripline commonly is referred to as a symmetric or “balanced” configuration. Such a symmetric or balanced two-conductor configuration readily supports differential signals on the coplanar stripline, as discussed further below; in contrast, the asymmetric or unbalanced configuration of the coplanar waveguide does not support differential signals, but merely supports “single-ended” signals (i.e., a signal that is referenced to a ground potential).
For many conventional microwave applications, coplanar waveguide implementations generally have been preferable as circuit interconnection structures due to the prevalence of primarily singled-ended or unbalanced microwave devices. Also, coplanar waveguides generally have been regarded as significantly less lossy than coplanar striplines, especially with respect to signal losses to the substrate at microwave frequencies. Hence, historically speaking, much of the relevant literature in connection with high frequency microelectronic devices has focused significantly more on coplanar waveguides rather than on coplanar striplines. Coplanar waveguides generally are regarded as easily integrated with both series and shunt active and passive circuit components. Moreover, the dimensions of coplanar waveguide conductors may be readily varied to match circuit component lead widths and thereby facilitate interconnection with other devices, while maintaining a desired characteristic impedance for the coplanar waveguide that is compatible with the interconnected devices. One tradeoff, however, is that coplanar waveguides take up significant space due to the relatively wide and multiple ground conductors flanking the center signal conductor.
Various characteristics of both coplanar waveguides and coplanar striplines may be modeled at least to some extent using common concepts related to electric circuit theory, such as resistance, inductance, conductance and capacitance. Wave-based structures in general, however, differ from ordinary electric networks in one essential feature: namely, size relative to operating frequency. For example, whereas the physical dimensions of electric networks are very much smaller than the wavelength corresponding to the operating frequency, the size of devices based on waveguides and transmission lines is usually a considerable fraction of the wavelength corresponding to the operating frequency of the device, and may even be many wavelengths long. Accordingly, whereas elements relating to resistance, inductance, conductance and capacitance may be described in common electric circuits as discrete components having lumped parameters, transmission lines and waveguides must instead be described by circuit parameters that are distributed throughout the length of the transmission line/waveguide.
In view of the foregoing, FIGS. 4A and 4B illustrate two different theoretical transmission line/waveguide models involving distributed “line parameters” based on electric circuit concepts. In particular, FIG. 4A shows a “single-ended” model 30 (which may be applied to the coplanar waveguide 50 illustrated in FIGS. 2A and 2B) and FIG. 4B shows a “differential” model 32 (which may be applied to the coplanar stripline 100 illustrated in FIGS. 3A and 3B).
In the models of FIGS. 4A and 4B, the parameter z indicates distance along a length of the transmission line/waveguide in the direction of wave propagation (where dz denotes differential length). The circuit-based line parameters are indicated in FIGS. 4A and 4B as resistance per unit length R, inductance per unit length L, conductance per unit length G, and capacitance per unit length C, wherein R and L are series elements and G and C are shunt elements. In FIG. 4B, the values attributed to the series elements R and L is are divided amongst two identical conductors of the model 32 (e.g., Rdz/2 and Ldz/2), to again indicate the “differential” nature of the model.
The line parameters R, L, G and C that may be used to characterize a coplanar waveguide or coplanar stripline directly result from the types of materials used to fabricate the coplanar stripline or coplanar waveguide (e.g., the dielectric, substrate, and metal components) and the various dimensions associated with the coplanar stripline or coplanar waveguide arrangement (e.g., width and thickness of the conductors, space between the conductors, thickness of the dielectric layer, etc.). More specifically, the materials and dimensions involved in a given structure generally determine various physical properties associated with the structure, such as effective permittivity εeff, permeability μ, and various loss factors, on which the line parameters R, L, G and C are based.
Again, as illustrated in FIGS. 4A and 4B, it should be appreciated that the line parameters R, L, G and C are not discrete or lumped but uniformly distributed along the entire length of the coplanar stripline or coplanar waveguide. Also, it should be appreciated that R is the AC resistance per unit length of the conductors (i.e., “series” resistance), whereas G is the conductance per unit length due to the dielectric medium separating the conductors from each other and the substrate (i.e., “shunt” resistance).
The distributed resistance, conductance, inductance and capacitance of the coplanar stripline or coplanar waveguide naturally result in particular frequency characteristics of a given implementation. For example, the general energy storage functions of both inductance and capacitance have a frequency dependence based on any resistance/conductance associated with the inductance/capacitance. One common parameter for characterizing the frequency response of a frequency dependent system, including a given transmission line (or waveguide) configuration, is referred to as a “quality factor,” typically denoted in the literature as Q.
The quality factor Q of a frequency dependent system generally is defined as a ratio of a peak or resonant frequency of the system to the frequency bandwidth of the system (i.e., the frequency range between the half-power points of the overall frequency response of the system). The quality factor Q alternatively may be viewed as a ratio of the maximum energy stored in the system to the total energy lost by the system in a given time period. In view of the foregoing, systems with a relatively large Q generally are viewed as being “frequency selective,” in that they support frequencies close to a given resonant frequency with relatively little energy loss. In contrast, systems with a relatively smaller Q do not necessarily have a significant frequency preference and are often viewed as somewhat lossy systems.
The quality factor Q of a given coplanar waveguide or coplanar stripline arrangement also may be expressed in terms of various parameters associated with the propagation of a wave along the coplanar waveguide or coplanar stripline. With reference again to the coplanar stripline 100 shown in FIG. 3B, an exemplary position-dependent voltage V(z) is indicated between the conductors and an exemplary position-dependent current I(z) is shown flowing through the conductors, where z indicates distance along the direction of wave propagation. The voltage V(z) as a function of position z along the coplanar stripline may be expressed as:V(z)=Voe−αz cos(2πft−βz),where Vo is the amplitude of the wave, and the quantity (2πft−βz) represents the phase (in radians) of the wave, which depends on both time t and space z. Of course, f is the frequency of the wave, and β is the “phase constant” of the wave, defined as β=2π/λ; essentially, the phase constant β indicates that for every wavelength of distance traveled, a wave undergoes a phase change of 2π radians. Finally, α is an attenuation factor representing losses as the wave propagates, which affect the overall amplitude of the wave; namely, as α increases, indicating greater loss, the amplitude Vo of the wave accordingly is decreased by the factor e−αz. As mentioned above, the quality factor Q also may be expressed in terms of the phase constant β and the attenuation factor α and approximated as Q≈β/2α for relatively low loss frequency dependent systems.
Another important characterizing parameter of transmission lines and waveguides relates to the speed with which waves propagate along the transmission line or waveguide. In particular, the phase velocity of a transmission line or waveguide, commonly denoted as v, provides the relationship between the frequency f and wavelength λ of a wave in a given medium, according to v=fλ, and represents the speed of wave propagation in the medium. Accordingly, for a given frequency f a smaller phase velocity v results in a shorter wavelength λ. The phase velocity v results from the particular physical characteristics of the device, such as effective permittivity εeff and permeability μ. With respect to the models illustrated in FIGS. 4A and 4B, the phase velocity may be expressed in terms of the inductance per unit length L and the capacitance per unit length C as v=1/√{square root over (LC)}.
Since reduction in circuit size generally is a significant goal of improved microelectronic device fabrication techniques, there has been focus in the literature in connection with size reduction of microwave devices based on features that facilitate a reduction in phase velocity. Again, a reduction in phase velocity results in a corresponding reduction in wavelength at a given operating frequency. Devices such as resonators, oscillators, impedance matching networks, signal splitters and combiners, filters, amplifiers and delays may be implemented based on transmission line or waveguide configurations. Often, as mentioned above, the size of such devices is comparable with the wavelength λ given a desired range of operating frequencies. Accordingly, by lowering the phase velocity v, smaller devices may be realized.
With this in mind, various “slow-wave” structures in the microwave field have been investigated since the 1970s. Again, many of these studies relate to monolithic microwave integrated circuits (MMICs) involving coplanar waveguides that incorporate features designed to decrease the phase velocity and wavelength, and hence device size, at a given operating frequency or range of frequencies. One such feature for realizing slow-wave structures includes a “periodically loaded” coplanar waveguide, in which floating metal strips are placed periodically beneath the three coplanar waveguide conductors and oriented transversely to the conductors. The presence of the floating metal strips generally is considered to spatially separate the electric and magnetic energy in the propagating wave, which results in an increased capacitance per unit length C of the coplanar waveguide. According to the relationship v=1/√{square root over (LC)}, such an increased capacitance per unit length C results in a smaller phase velocity v, and hence a smaller wavelength λ at a given frequency f Thus, the presence of these slow-wave features may facilitate fabrication of smaller devices.
In conventional slow-wave microwave structures based on coplanar waveguides, a reduction in wavelength β results in a corresponding increase in the phase constant β, pursuant to the relationship β=2π/λ. However, the effect of increased phase constant β on the quality factor Q, according to the relationship Q≈β/2α, is not entirely clear from the literature; while an increase in Q might be expected from an increase in β, the effect of the slow-wave features on the loss α of the coplanar waveguide is unclear. In some reports, it has been suggested that the Q of a coplanar waveguide slow-wave structure incorporating floating metal strips actually may decrease from that of a coplanar waveguide without the slow-wave features, due to increased loss a resulting from the presence of the slow-wave features. Thus, it appears that there may be a tradeoff between quality factor and phase velocity in some coplanar waveguide slow-wave structures; namely, that while phase velocity may be reduced to facilitate implementation of smaller devices, greater losses may result, thereby degrading the quality factor Q of the device.